2012/12/31 by Jean‐Luc Marichal, Jean-Luc Marichal, Bruno Teheux
Computer Science · Mathematics · #Advanced Algebra and Logic #Artificial intelligence #Boolean function #Class (philosophy) #Combinatorics #Computer science #Discrete mathematics #Function (biology) #Lattice (music) #Mathematical analysis #Mathematics #Multilinear map #Polynomial #Pure mathematics #Rough Sets and Fuzzy Logic #Unary operation #cs.DM #math.RA #msc:94C10 #semigroups and automata theory
paper · pdf · doi:10.1016/j.dam.2014.04.013
published as Discrete Applied Mathematics 174 (2014) 102-112
openalex publication_date 2014/05/01 · arxiv created 2014/06/07 · arxiv updated 2014/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon its values at two given elements. Pivotal decompositions appear to hold for various function classes, such as the class of lattice polynomial functions or the class of multilinear polynomial functions. We also define function classes characterized by pivotal decompositions and function classes characterized by their unary members and investigate links between these two concepts.